Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13370 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C23×C17 | AGL(1,ℤ/8) |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
358 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,23)(20,24,25,22)(26,27)(28,37)(29,43)(30,35)(31,48)(32,36)(33,39)(34,46)(38,53)(40,50)(41,57)(42,55)(44,52)(45,51)(47,54)(49,56);(18,20,21,25)(19,22,23,24)(26,27)(28,38)(29,34)(30,48)(31,35)(32,36)(33,40)(37,53)(39,50)(41,49)(42,52)(43,46)(44,55)(45,54)(47,51)(56,57);(26,28,32,42)(27,33,36,49)(29,44,47,53)(30,41,31,40)(34,50,51,57)(35,52,48,38)(37,54,55,43)(39,45,56,46)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6358);